To find the GCF one must find the factors of two numbers.  For example if you were given 18 and 24, the factors of 18 are (1,2,3,6,9,18)  and the factors of 24 are (1,2,3,4,6,8,12,24)  The number 6 is the Greatest Common or like Factor.  All the numbers in parenthesis are a multiple of the number ie.  2x9 = 18, 1x18 =18, 3x6 =18.

For example an equivalent fraction would be: 1/2, 2/4, 3/6 and 4/8.

Also, another way to determine an equivalent fraction, for example with a denominator of 12, would be to multiply the current denominator with the multiplier of that denominator.

Thusly:  1/4  would be = to 3/12, because  3 when multiplied by 4 = 12 and then 3 when multiplied with 1 = 3.

Or: 2/3 would be = to 8/12, because 4 when multiplied by the denominator = 12 and 4 when multiplied by the numerator = 8

We will be looking at mixed numbers in fractions and improper. 

This fraction is a mixed fraction  3 1/2

This fraction is an improper fraction  11/3.  An improper fractions numerator is bigger than the denominator.

To convert a mixed fraction to an improper fraction, multiply the whole number by the denominator and add the numerator.  So 3 1/2  equals  3 x 2 = 6, add 1 to that which equals 7.  7 is your new numerator and use the same denominator of 2.  So your improper fraction is 7/2.

To convert an improper fraction to a mixed number take  11/3 and divide using your traditional way to divide.

3 goes into 11, 3 times; multiply 3 x 3 = 9, subtract 9 from 11 with a remainder of 2.  Thus your fraction is now

3 and 2/3.

How to find the LCD or Least Common Denominator

If you were asked to find the LCD of two fractions you would either have to multiply the two denominators together or find the lowest multiple, not factor, of two given numbers. Also, if the LCD is not evident after multiplying the two denominators than looking at all of the factors will determine the least or lowest common number.  An example of this would be: 2/6 and 3/9.  You need to know all the multiples of each.  You would not want to multiply the two denominators to get 54.  Instead the multiples of 6 are: 6,12,18,24,30 etc and the multiples of 9 are: 9,18,27,36 etc.  Here you can see that 18 is in both groups, is the lowest same number, so this is the LCD to be used.

 For example, if I had to add 1/2 and 2/3 together I could multiply the 2 x 3 and get 6 as my new denominator.  I then would ask myself how many times will 2 ( from the 1/2) go into 6.  The answer is 3.  I then would multiply the 1 (from the 1/2) by 3 and get 3.  My new fraction from the original 1/2 would now be 3/6.  I would then do the same steps for 2/3.  3 goes into 6, 2 times, and 2 times 2 = 4.  My new fraction (for 2/3) is now 4/6.  I now can add the two numerators from 3/6 and 4/6 and get 7/6.  THIS IS AN IMPROPER FRACTION.  So you then must convert it to a MIXED FRACTION.

You also can find the LCD of two fractions by writing out the multiples for each denominator.  For example, I have  to add 3/12 and 4/24.  I would not multiply the 12 x 24, but use 24 as my denominator because 12 goes into 24.  I would then follow the above steps for multiplying to find the new numerators.

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 LINEAR MEASUREMENT

Students need to memorize these measurements.

A standard 12 inch ruler is divided into measurement segments or fractions.  A ruler is broken down from 1 whole or inch, to halves 1/2, quarters 1/4, eighths 1/8 and sixteenths 1/16.  There are two (1/2s), four (1/4ths), eight (1/8ths) and 16 (1/16ths).  Each student should be able tell how a fraction could be read as quarters or eighths.  If given the fraction of 2 and 2/4, they should be able to tell me that there are also 10 fourths.  Also, if given the fraction of 2 4/16, they can tell me that there are 36/16th.

1 foot  or 1' = 12 inches or 12"

1 yard = 3'  or 36 "

1 mile = 5280' or 1760 yards or 63,360 "

Students need to be able to convert accordingly.

                                                                              CIRCUMFERENCE

TO FIND THE CIRCUMFERENCE OF A CIRCLE USING ITS DIAMETER USE THIS FORMULA WITH pi:

C = ∏   X  D                   * ∏ = 3.14 

FOR RADIUS USE:    C = 2 X  ∏  X  R     

                                                                                                                                     VOLUME

VOLUME = LENGTH  X  WIDTH  X  HEIGHT

Geometry and Polygons

We have begun to explore geometry this month.  Students are expected to understand geometry vocabulary.   They need to know what a line, ray, an angle and a vertex and endpoint are.  Also they need to know types of lines, whether they are parallel, intersecting, or perpendicular.  Secondly, students need to know how to label an angle and measure it using a protractor.  Thirdly, students will define whether the angle is acute, right or a obtuse.  An acute angle is less than 90 degrees, a right angle is 90 degrees and an obtuse angle is greater than 90 degrees.  Angles are formed in polygons.  Polygons are made up of connecting lines or sides.  Polygons are triangular - three sided (equilateral, isosceles or scalene).  Polygons are found in quadrilaterals, they are four sided.  Polygons come in a square, rectangle, parallelogram, rhombus and trapezoid shape.

Polygons are congruent - same size and shape. Or similar same shape but can be different sized.  Shapes, as in a pentomino, can be flipped, turned, slid or lined up.  Students will also learn the line of symmetry.

Go to   http://www.mathisfun.com  for practice with polygons.

Multiplication

  Distributive property of multiplication will also be explored.  When you use distributive property you break the numbers down into smaller chunks.

An example of distributive property is this:

If the dog sled teams on one of the Arctic expeditions traveled 19 miles a day for 6 days, how far did they travel?

To find the distance traveled in 6 days, multiply.

 6 x 19

6 x 19 = 6 x (10 + 9)      break 19 apart.

= (6 x 10) + (6 x 9)    19 = 10 + 9

= 60 + 54                                      

 = 114      

6 x 19 = 114                                       

The teams traveled 114 miles in 6 days.